
Mount Takao is almost suspiciously easy to reach: one direct train from Shinjuku, about 50 minutes, a few hundred yen, and the station sits right at the trailhead. Here's the cleanest way and the ticket worth buying.
If you'll ride the cable car or chairlift up, the Keio 'Takao discount ticket' bundles the round-trip train with the cable car and saves a little. Tap an IC card otherwise. On weekend mornings everyone arrives 9–10am and the cable-car line backs up — come earlier, or take a walking trail up instead.
Take the Keio line direct from Shinjuku to Takaosanguchi — about 50 minutes, ~¥400, no transfers. The station is a 5-minute walk from the cable car and trailhead.
Yes — the Keio Takao discount ticket bundles the round-trip train with the cable car or chairlift, saving a little if you ride up rather than walk.